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IPI
We consider the AKNS (Ablowitz-Kaup-Newell-Segur) operator on the unit
interval with potentials belonging to Sobolev spaces in the framework of
inverse spectral theory. Precise sets of eigenvalues are given in order
that they, together with the knowledge of the potentials on
the side $(a,1)$ and partial informations on the potential on $(a-\varepsilon,a)$ for some arbitrary small
$\varepsilon>0$,
determine the
potentials entirely on $(0,1)$. Naturally, the smaller is $a$ and
the more partial informations are known, the less is the number of the needed
eigenvalues.
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